A description is given of a process for preparing solutions of radiation-sensitive, free-radically polymerizable organic compounds, where a first starting compound, which has an acid halide group, and a second starting compound, which has an alcoholic hydroxyl group, are esterified with one another in a solvent or in a solvent mixture. The solvent comprises one or more ketones having a boiling point of below 150° C. under atmospheric pressure (1 bar), or the solvent mixture is composed to an extent of at least 50% by weight of said ketones. One of the two starting compounds has at least one radiation-sensitive group and the other of the two starting compounds has at least one ethylenically unsaturated, free-radically polymerizable group. A description is also given of corresponding solutions of radiation-sensitive, free-radically polymerizable organic compounds and of their use for preparing radiation-crosslinkable, free-radically copolymerized copolymers, more particularly for hotmelt pressure-sensitive adhesives or aqueous polymer dispersions.